VBTutorial1

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Basics of VB theory and XMVB program

Remarks

>> Initial remarks for tutors

Exercises

Exercise 1 (paper exercise) : The lone pairs of H<math>{}_2</math>O

This exercise aims at comparing two descriptions of the lone pairs of H<math>{}_2</math>O : (i) the MO description in terms of non-equivalent canonical MOs and (ii) the « rabbit-ear » VB description in terms of two equivalent hybrid orbitals.

<math>\Psi_{\textrm{MO}}</math>   <math>\Psi_{\textrm{VB}}</math>

1. Focusing on the lone pairs only, write the four-electron single-determinants <math>\Psi_{\textrm{MO}} </math> and <math>\Psi_{\textrm{VB}} </math> .
2. Expand <math>\Psi_{\textrm{VB}} </math> into elementary determinants containing only <math>n</math> and <math>p</math> orbitals, eliminate determinants having two identical spinorbitals, and show the equivalence between <math>\Psi_{\textrm{VB}}</math> and <math>\Psi_{\textrm{MO}}</math>.
3. We now remove one electron from H<math>{}_2</math>O. Write the two possible VB structures <math>\Phi_1</math> and <math>\Phi_2</math> in the VB framework.
4. The two ionized states are the symmetry-adapted combinations <math>\frac{1}{2}\left(\Phi_1-\Phi_2\right)</math> and <math>\frac{1}{2}\left(\Phi_1+\Phi_2\right)</math>. From the sign of the hamiltonian matrix element <math>\langle \Phi_1 \vert \hat{H} \vert \Phi_2 \rangle</math>, give the energy ordering of the two ionized states.
5. By expanding the two ionized states into elementary determinants (dropping the normalization constants), show that they are equivalent, respectively, to the MO configurations <math>\vert nn\bar{p}\vert</math> and <math>\vert pp\bar{n}\vert</math>.

Appendix

Hamiltonian matrix element between determinants differing by one spin-orbital :

<math>\langle \cdots i \cdots \vert \hat{H} \vert \cdots j \cdots\rangle = \beta_{ij}</math>

>> Answer

Exercise 2 : Starting up with the H2 molecule

Two Gamess and XMVB input files for the H2 molecule are provided in the Exercise folder on the tutorial machines :

• the file h2-atom.xmi input uses the fragment specification in terms of atoms (frgtyp=atom) ;
• the file h2-sao.xmi input uses the fragment specification in terms of symmetry-adapted orbitals (frgtyp=sao).

There are VBSCF calculations with the 6-31G(d,p) basis set. Just inspect these inputs, run the gamess-xmvb program (using : vbrun h2-atom and : vbrun h2-sao, and inspect the outputs.

Then these input files could serve you as templates for the next exercises.

Exercise 3 : HF molecule : weights and bond energy

1. Compute a VBSCF three structure wave function for the HF molecule, using the frgtyp=sao specification and automatic guess (guess=auto). Which structure(s) should be kept in further BOVB calculations ?
2. Using VBSCF orbitals as guess orbitals :
   1. Compute a L-BOVB wave function on a selected subset of structures ;
   2. Compute a VBCISD wave function for the multi-structure wave function
   3. Compare structure weights at the VBSCF, L-BOVB and VBCI levels
3. Compute bond energies at the L-BOVB and VBCISD levels.

>> Hints and remarks

Exercice 3 : Dissociation of C(Me)3-Cl and solvent effect

Subject

First calculation beyond diatomics (fragment C(Me)3 and Cl). VB(PCM) method.

To do

• Compute of C(Me)3-Cl at equilibrium distance at the VBSCF and D-BOVB levels.
• Compute C(Me)3-Cl at large inter fragment distance (5Å ?), at the D-BOVB level.
• Redo previous questions using the VB(PCM) option.

Access to files :

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